Numerical Data Analysis

A measured reflection profile or diffraction pattern essentially consists of a set of N data couples of intensities 1; collected at scattering angles 2O. All physical parameters derived from it, like unit cell edges, crystallite size or average microstrain, are based on the adaptation of the data to a physical or a microstructural model. The aspects of structural modeling are shown schematically in Fig. i4.1. Often the experimentalist is interestedin the preparation of thin films with optimized physical properties (lower right box),which are governed by the structural and microstructural properties of the layer-substrate system (upper box). To the same extent the x-ray(x ray protection) scattering pattern (lower left box) is determined by the specimen's structure. In order to elicit certain material properties the structure has to be deduced from the pattern, which can be considered as the inverse problem of thin-film analysis by x-ray scattering.
The model should allow for the formulation(disabled supplies) of a theoretical intensity function y(20, x) depending on a set of P parameters x,. The Cauchy function with parameters x- (10, 2Bo, 2w) or any other of the profile functions of Section 3.1 may serve as examples. It is realized from their analytical expressions that the parameters may be linearly (10) or nonlinearly (280, 2w) related to the model function. A model function for microstructural analysis by whole pattern fitting may comprise the parameter vector x- (a0, pt, D0, Iny, pd).If only one nonlinear parameter occurs in x, nonlinear techniques are required for the solution. The task to be solved is the identification of parameter values x} that optimally describe the set of measured intensities 1;. If the errors of the measurement are equally distributed "optimum" parameters follow from the minimization of the chi-square function.

Numerical Data Analysis

A measured reflection profile or diffraction pattern essentially consists of a set of N data couples of intensities 1; collected at scattering angles 2O. All physical parameters derived from it, like unit cell edges, crystallite size or average microstrain, are based on the adaptation of the data to a physical or a microstructural model. The aspects of structural modeling are shown schematically in Fig. i4.1. Often the experimentalist is interestedin the preparation of thin films with optimized physical properties (lower right box),which are governed by the structural and microstructural properties of the layer-substrate system (upper box). To the same extent the x-ray(x ray protection) scattering pattern (lower left box) is determined by the specimen's structure. In order to elicit certain material properties the structure has to be deduced from the pattern, which can be considered as the inverse problem of thin-film analysis by x-ray scattering.
The model should allow for the formulation(disabled supplies) of a theoretical intensity function y(20, x) depending on a set of P parameters x,. The Cauchy function with parameters x- (10, 2Bo, 2w) or any other of the profile functions of Section 3.1 may serve as examples. It is realized from their analytical expressions that the parameters may be linearly (10) or nonlinearly (280, 2w) related to the model function. A model function for microstructural analysis by whole pattern fitting may comprise the parameter vector x- (a0, pt, D0, Iny, pd).If only one nonlinear parameter occurs in x, nonlinear techniques are required for the solution. The task to be solved is the identification of parameter values x} that optimally describe the set of measured intensities 1;. If the errors of the measurement are equally distributed "optimum" parameters follow from the minimization of the chi-square function.

First-time visitors to Riding for the Disabled in "awe"

A FAMILY fun day was a hit with visitors to a charity last week.
East Park Riding for the Disabled (disabled products), based at Little Brook Equestrian Centre in Newchapel, teaches children with disabilities to ride horses and ponies.
Alan Maguinness, Santander's East Grinstead branch manager, was among the first-time guests.
The bank donated £4,000 to the charity to enable them to invest in a new horse, called Archie.
He said: "I have never been here before and I am completely overwhelmed with what they do here.
"Seeing the children on the horses and seeing their faces light up is absolutely amazing."
Horley Lions have been raising money for the charity for 23 years, and this year Andrew Harper, chairman of activities for the Lions, also visited the venue for the first time.
He said: "I am completely in awe of what Sally [the owner] has done here. The volunteers work tirelessly so the children get the best out of the experience.
"I think this gives them a sense of independence that they might not otherwise have if they are confined to a chair.".
Chairman of Tandridge District Council Beverley Connolly added: "I have never been here before and I think it is important to know what is going on in Tandridge. I think it is absolutely wonderful what they do here. Seeing a child gain independence and confidence(elbow crutches for sale) is just amazing."
Owner Sally O'Neill said she was sad that the charity's patron, Dame Judi Dench, who had been scheduled to attend, could not make it.
She said: "She is truly passionate about what we do here and we hope she will pop along again soon. I know she is quite upset she could not be here to see the children and horses.
"But, it has been a fantastic day and I think it has been amazing that other people have seen what we do."

First-time visitors to Riding for the Disabled in "awe"

A FAMILY fun day was a hit with visitors to a charity last week.
East Park Riding for the Disabled (disabled products), based at Little Brook Equestrian Centre in Newchapel, teaches children with disabilities to ride horses and ponies.
Alan Maguinness, Santander's East Grinstead branch manager, was among the first-time guests.
The bank donated £4,000 to the charity to enable them to invest in a new horse, called Archie.
He said: "I have never been here before and I am completely overwhelmed with what they do here.
"Seeing the children on the horses and seeing their faces light up is absolutely amazing."
Horley Lions have been raising money for the charity for 23 years, and this year Andrew Harper, chairman of activities for the Lions, also visited the venue for the first time.
He said: "I am completely in awe of what Sally [the owner] has done here. The volunteers work tirelessly so the children get the best out of the experience.
"I think this gives them a sense of independence that they might not otherwise have if they are confined to a chair.".
Chairman of Tandridge District Council Beverley Connolly added: "I have never been here before and I think it is important to know what is going on in Tandridge. I think it is absolutely wonderful what they do here. Seeing a child gain independence and confidence(elbow crutches for sale) is just amazing."
Owner Sally O'Neill said she was sad that the charity's patron, Dame Judi Dench, who had been scheduled to attend, could not make it.
She said: "She is truly passionate about what we do here and we hope she will pop along again soon. I know she is quite upset she could not be here to see the children and horses.
"But, it has been a fantastic day and I think it has been amazing that other people have seen what we do."

Medical device company MedaPhor signs deal to sell instruments in China

Cardiff medical devices company MedaPhor has entered into a new distribution deal that will see its innovative products sold in China. 
The Cardiff University spinout firm, which has received equity backing from Fusion IP, has developed technology that provides medical(cheap medical equipment) students with a training programme that replicates a real ultrasound scanning experience. 
Trainees can feel what they see on the computer screen in order to develop the complex mix of cognitive skills and eye-hand movement co-ordination, but without the need for an ultrasound machine or a patient and with considerably reduced direct supervision by an expert. 
It has now entered into a exclusive distribution agreement with Tellyes Scientific, which will see its range of ultrasound simulators into mainland China. 
Tellyes, a $40m medical simulation manufacturing and distribution business, based in Tianjin in China, has 100 dedicated sales staff. 
As part of the agreement Tellyes is purchasing 10 of MedaPhor’s ScanTrainer systems that will be sited in its five regional offices that cover the whole of China Tellyes will be targeting China’s 3,000 nursing schools, medical colleges and universities. 
Since spinning out of Cardiff University, MedaPhor has established sales in the UK, Europe, Australia and the US and recently expanded its ScanTrainer range with its new transabdominal simulator, aimed at the large obstetrics and gynaecology, general medical, and emergency medicine markets. 
Fusion has a 39% shareholding in MedaPhor. 
Chief executive of Tellyes, Simon Liu said: “We are very excited about the newly-formed strategic partnership with MedaPhor, whose ultrasound(portable ultrasound machine) simulators are great additions to what Tellyes is currently offering to the Chinese hospitals and medical schools.” 
Stuart Gall, chief executive of MedaPhor, said: “We are delighted to be working with Tellyes to target the huge and growing Chinese medical simulation market and we look forward to working with Simon and his team, as we launch our range of ScanTrainer simulator systems into China.” 
Chief executive of Fusion IP, David Barnes, said: “This is a major development for MedaPhor and we are excited about the potential of the Chinese market for MedaPhor’s superb ultrasound simulator. 
MedaPhor is now generating sales in all the major global medical markets and we look forward to its continued growth.”

Medical device company MedaPhor signs deal to sell instruments in China

Cardiff medical devices company MedaPhor has entered into a new distribution deal that will see its innovative products sold in China. 
The Cardiff University spinout firm, which has received equity backing from Fusion IP, has developed technology that provides medical(cheap medical equipment) students with a training programme that replicates a real ultrasound scanning experience. 
Trainees can feel what they see on the computer screen in order to develop the complex mix of cognitive skills and eye-hand movement co-ordination, but without the need for an ultrasound machine or a patient and with considerably reduced direct supervision by an expert. 
It has now entered into a exclusive distribution agreement with Tellyes Scientific, which will see its range of ultrasound simulators into mainland China. 
Tellyes, a $40m medical simulation manufacturing and distribution business, based in Tianjin in China, has 100 dedicated sales staff. 
As part of the agreement Tellyes is purchasing 10 of MedaPhor’s ScanTrainer systems that will be sited in its five regional offices that cover the whole of China Tellyes will be targeting China’s 3,000 nursing schools, medical colleges and universities. 
Since spinning out of Cardiff University, MedaPhor has established sales in the UK, Europe, Australia and the US and recently expanded its ScanTrainer range with its new transabdominal simulator, aimed at the large obstetrics and gynaecology, general medical, and emergency medicine markets. 
Fusion has a 39% shareholding in MedaPhor. 
Chief executive of Tellyes, Simon Liu said: “We are very excited about the newly-formed strategic partnership with MedaPhor, whose ultrasound(portable ultrasound machine) simulators are great additions to what Tellyes is currently offering to the Chinese hospitals and medical schools.” 
Stuart Gall, chief executive of MedaPhor, said: “We are delighted to be working with Tellyes to target the huge and growing Chinese medical simulation market and we look forward to working with Simon and his team, as we launch our range of ScanTrainer simulator systems into China.” 
Chief executive of Fusion IP, David Barnes, said: “This is a major development for MedaPhor and we are excited about the potential of the Chinese market for MedaPhor’s superb ultrasound simulator. 
MedaPhor is now generating sales in all the major global medical markets and we look forward to its continued growth.”

Emotional farewell to Marathon memorial

Survivors and family members of those killed when two bombs exploded at the Boston Marathon gathered Monday evening for one last look at a spontaneous public memorial in Copley Square commemorating the dead and injured.
Among the flowers, banners, handmade signs, and running shoes, they stood and sat, many using crutches(pair of crutches) and several in wheelchairs, for a brief prayer service under a pair of orange canopies.
Sarah Rothenberg, a Boylston Street resident who witnessed the bombings from her apartment, said she was among those invited by city officials to attend the ceremony but preferred to remain behind police barricades erected to give the survivors and the families privacy.
“Any opportunity I have to show my support for Boston and for the victims, I’m there,” said Rothenberg, 28, a kindergarten teacher.
Rothenberg said she had been excited to have an apartment with four large windows overlooking Boylston Street and had invited many friends and family to a viewing party.
“We were all sitting in the windows, watching the finish line, and what started off as such a beautiful celebration turned so horrible,” she said. “It was unreal.”
Rothenberg said she has visited the memorial many times and left her own handwritten message to the victims of the bombings.
She is surrounded by reminders of the violence, she said. As a runner, she regularly passes the sites where both bombs exploded.
“It used to just be those spots I’d run by and I’d never think about it, and now I’m reminded every day of what happened,” she said.
Mayor Thomas M. Menino said in a June 17 letter to survivors and victims’ families that city workers would dismantle the memorial Tuesday and move the items to the city archives in West Roxbury for cleaning, fumigation, and archiving.
Members of the Richard family of Dorchester attended the ceremony, a rare public appearance by a family devastated by the attack.
Martin Richard, who would have turned 9 this month, was killed in the blasts. His sister, Jane, 7, lost a leg. Denise, the children’s mother, suffered a head injury and lost vision in an eye. Their father, Bill, received shrapnel wounds and suffered hearing loss. The eldest child, Henry, was unharmed.
Reporters and onlookers were asked to remain across the street during the ceremony, out of respect for the survivors and victims’ families.
Dot Joyce, the mayor’s spokeswoman, said the prayer service was led by the Rev. Samuel T. Lloyd III, priest in charge at Trinity Church, and Nancy S. Taylor, senior minister at Old South Church. It included remarks from Menino and Dr. Barbara Ferrer, the city’s commissioner of public health, who helped organize the event, she said.
“This was an opportunity for survivors and families to have a chance to privately . . . view the memorial, remove any personal items that may have been left for them specifically, and participate in a very brief prayer service,” Joyce said.
Milton resident David Stokle, 48, said he ran his first Boston Marathon unofficially when he was in the eighth grade and hopes to run once more when he turns 50.
He compared the innocent victims of the bombing to nine climbers killed Sunday in Pakistan on that country’s second-highest mountain. The Pakistani Taliban claimed responsibility for the attack.
“I hope that they do put a small sculpture [in Copley Square], maybe a small replica of a metal fence with some shoes on it, so that we can remember the people who suffered,” said Stokle. “And the people who caused other people to suffer could see that and might reflect upon what they did.”
Survivors Adrianne Haslet, a dance instructor who lost part of her left leg(disabled products), and her husband, Air Force Captain Adam Davis, who had served in Afghanistan, lingered after the ceremony.
As others filed onto buses provided by the city, Haslet sat on the ground inside the memorial area, writing a message on a large banner.
The evening was muggy and hot, with temperatures remaining in the high 80s throughout the ceremony. Kat Powers was present with the American Red Cross of Eastern Massachusetts, alongside 12 disaster mental health volunteers invited by the city, and helped hand out water bottles and tissues.
“I saw a lot of hugs,” she said. “This was a nice way for the families to have some privacy, their own thoughts.”
Around 7:30 p.m., police removed the barricades and allowed the public back into the memorial for one last look.

Emotional farewell to Marathon memorial

Survivors and family members of those killed when two bombs exploded at the Boston Marathon gathered Monday evening for one last look at a spontaneous public memorial in Copley Square commemorating the dead and injured.
Among the flowers, banners, handmade signs, and running shoes, they stood and sat, many using crutches(pair of crutches) and several in wheelchairs, for a brief prayer service under a pair of orange canopies.
Sarah Rothenberg, a Boylston Street resident who witnessed the bombings from her apartment, said she was among those invited by city officials to attend the ceremony but preferred to remain behind police barricades erected to give the survivors and the families privacy.
“Any opportunity I have to show my support for Boston and for the victims, I’m there,” said Rothenberg, 28, a kindergarten teacher.
Rothenberg said she had been excited to have an apartment with four large windows overlooking Boylston Street and had invited many friends and family to a viewing party.
“We were all sitting in the windows, watching the finish line, and what started off as such a beautiful celebration turned so horrible,” she said. “It was unreal.”
Rothenberg said she has visited the memorial many times and left her own handwritten message to the victims of the bombings.
She is surrounded by reminders of the violence, she said. As a runner, she regularly passes the sites where both bombs exploded.
“It used to just be those spots I’d run by and I’d never think about it, and now I’m reminded every day of what happened,” she said.
Mayor Thomas M. Menino said in a June 17 letter to survivors and victims’ families that city workers would dismantle the memorial Tuesday and move the items to the city archives in West Roxbury for cleaning, fumigation, and archiving.
Members of the Richard family of Dorchester attended the ceremony, a rare public appearance by a family devastated by the attack.
Martin Richard, who would have turned 9 this month, was killed in the blasts. His sister, Jane, 7, lost a leg. Denise, the children’s mother, suffered a head injury and lost vision in an eye. Their father, Bill, received shrapnel wounds and suffered hearing loss. The eldest child, Henry, was unharmed.
Reporters and onlookers were asked to remain across the street during the ceremony, out of respect for the survivors and victims’ families.
Dot Joyce, the mayor’s spokeswoman, said the prayer service was led by the Rev. Samuel T. Lloyd III, priest in charge at Trinity Church, and Nancy S. Taylor, senior minister at Old South Church. It included remarks from Menino and Dr. Barbara Ferrer, the city’s commissioner of public health, who helped organize the event, she said.
“This was an opportunity for survivors and families to have a chance to privately . . . view the memorial, remove any personal items that may have been left for them specifically, and participate in a very brief prayer service,” Joyce said.
Milton resident David Stokle, 48, said he ran his first Boston Marathon unofficially when he was in the eighth grade and hopes to run once more when he turns 50.
He compared the innocent victims of the bombing to nine climbers killed Sunday in Pakistan on that country’s second-highest mountain. The Pakistani Taliban claimed responsibility for the attack.
“I hope that they do put a small sculpture [in Copley Square], maybe a small replica of a metal fence with some shoes on it, so that we can remember the people who suffered,” said Stokle. “And the people who caused other people to suffer could see that and might reflect upon what they did.”
Survivors Adrianne Haslet, a dance instructor who lost part of her left leg(disabled products), and her husband, Air Force Captain Adam Davis, who had served in Afghanistan, lingered after the ceremony.
As others filed onto buses provided by the city, Haslet sat on the ground inside the memorial area, writing a message on a large banner.
The evening was muggy and hot, with temperatures remaining in the high 80s throughout the ceremony. Kat Powers was present with the American Red Cross of Eastern Massachusetts, alongside 12 disaster mental health volunteers invited by the city, and helped hand out water bottles and tissues.
“I saw a lot of hugs,” she said. “This was a nice way for the families to have some privacy, their own thoughts.”
Around 7:30 p.m., police removed the barricades and allowed the public back into the memorial for one last look.

The Basic Phenomenon

Before the geometrical constraints for x-ray(x ray protection) interference are derived the interactions between x-rays and matter have to be considered. There are three different types of interaction in the relevant energy range. In the first, electrons may be liberated from their bound atomic states in the process of photoionization. Since energy and momentum are transferred from the incoming radiation to the excited electron, photoionization falls into the group of inelastic scattering processes. In addition, there exists a second kind of inelastic scattering that the incoming x-ray beams may undergo, which is termed Compton scattering. Also in this process energy is transferred to an electron, which proceeds,however, without releasing the electron from the atom. Finally, x-rays may be scattered elastically by electrons,which is named Thomson scattering. In this latter process the electron oscillates like a Hertz dipole at the frequency ofthe incoming beam and becomes a source of dipole radiation. The wavelength A of x-rays is conserved for Thomson scattering in contrast to the two inelastic scattering processes mentioned above.It is the Thomson component in the scattering ofx-rays that is made use of in structural investigations by x-ray diffraction. Figure 1.1 illustrates the process of elastic scattering for a single free electron of charge e, mass m and at position R0. The incoming beam is accounted for by a plane wave #oexp(-iKKR4), where FO is the electrical field vector and Ko the wave vector. The dependence of the field on time will be neglected throughout. The wave vectors KO and K describe the direction of the incoming and exiting beam and both are of magnitude 2Y/3.. They play an important role in the geometry of the scattering process and the plane defined by them is denoted as the scattering plane. The angle between K and the prolonged direction of Ko is the scattering angle that will be abbreviated by 20 as is general use in x-ray diffraction. We may also define it by the two wave vectors according to
20 = arccos (K,K0}/KK0
The formula is explicitly given here, because the definition of angles by two adjoining vectors will be made use of frequently.The oscillating charge a will emit radiation of the same wavelength A as the primary beam. In fact, a phase shift of 180' occurs with the scattering, but since this shift equally arises for every scattered wave it has no effect on the interference pattern in which we are interested and will be neglected. If the amplitude of the scattered wave E(R)(portable ultrasound machine) is considered at a distance R we may write according to Hertz and Thomson.

The Basic Phenomenon

Before the geometrical constraints for x-ray(x ray protection) interference are derived the interactions between x-rays and matter have to be considered. There are three different types of interaction in the relevant energy range. In the first, electrons may be liberated from their bound atomic states in the process of photoionization. Since energy and momentum are transferred from the incoming radiation to the excited electron, photoionization falls into the group of inelastic scattering processes. In addition, there exists a second kind of inelastic scattering that the incoming x-ray beams may undergo, which is termed Compton scattering. Also in this process energy is transferred to an electron, which proceeds,however, without releasing the electron from the atom. Finally, x-rays may be scattered elastically by electrons,which is named Thomson scattering. In this latter process the electron oscillates like a Hertz dipole at the frequency ofthe incoming beam and becomes a source of dipole radiation. The wavelength A of x-rays is conserved for Thomson scattering in contrast to the two inelastic scattering processes mentioned above.It is the Thomson component in the scattering ofx-rays that is made use of in structural investigations by x-ray diffraction. Figure 1.1 illustrates the process of elastic scattering for a single free electron of charge e, mass m and at position R0. The incoming beam is accounted for by a plane wave #oexp(-iKKR4), where FO is the electrical field vector and Ko the wave vector. The dependence of the field on time will be neglected throughout. The wave vectors KO and K describe the direction of the incoming and exiting beam and both are of magnitude 2Y/3.. They play an important role in the geometry of the scattering process and the plane defined by them is denoted as the scattering plane. The angle between K and the prolonged direction of Ko is the scattering angle that will be abbreviated by 20 as is general use in x-ray diffraction. We may also define it by the two wave vectors according to
20 = arccos (K,K0}/KK0
The formula is explicitly given here, because the definition of angles by two adjoining vectors will be made use of frequently.The oscillating charge a will emit radiation of the same wavelength A as the primary beam. In fact, a phase shift of 180' occurs with the scattering, but since this shift equally arises for every scattered wave it has no effect on the interference pattern in which we are interested and will be neglected. If the amplitude of the scattered wave E(R)(portable ultrasound machine) is considered at a distance R we may write according to Hertz and Thomson.

Line Profile Analysis

Soon after the invention of x-ray(x ray protection) diffraction it became dear that the method was not only suited to resolve crystalline structures, but could also reveal information on a sample's microstructure. In 1918 Scherrer devised a formula describing how the width of a Bragg reflection increases with decreasing crystallite size. The formula became very popular in the investigation of polycrystalline samples and made the crystallite size-peak width relation an ongoing issue in x-ray diffraction. It has to be emphasized, however, that the crystallite size derived from x-ray peak profiles accounts for domain sizes that scatter the incoming x-rays coherently. The size of coherently diffracting domains is generally smaller than the crystallite size as obtained by other techniques like transmission electron microscopy. It thus has to be carefully specified as to which experimental quantity is exactly meant whenever crystallite sizes are compared that have been obtained by different techniques.


The width of Bragg reflections was also realized to be affected by microstructural features other than size broadening, like the crystallite shape, the shape distribution and any distortion of the crystal structure like microstrain, dislocations,twin planes and stacking faults. The general question in the microstructural analysis of polycrystals relates to how the physical properties of the specimen are affected by its microstructure. It is evident that the microstructural richness of a polycrystalline thin film can become a hard task to be fully elucidated. The investigations are thus often restricted to certain aspects like the density of certain lattice faults.


Microstrain and dislocations play a prominent role in the various distortions of the crystal lattice. In the vicinity of dislocations the atoms reside on equilibrium po- sitions distinct from those in the unperturbed lattice and cause the surrounding bond lengths to contract and expand. The strain fields introduced by dislocations may extend over many hundreds of unit cells in the crystal. The interplanar spacing d as it appears in the Bragg equation is thus subjected to a variation and may not be accounted for by a fixed value do, but by a distribution of d values. The strain fields thus cause a smearing of scattered x-ray intensity around do and a broadening of reflections. These strain fields are denoted as microstrain, because they appear on a length scale that is small when compared with the inverse linear attenuation coefficient, 1/5, of the probing x ray beam. Although this definition is rather unsatisfactory, because a sample property is related to the technique by which it is probed, it is a practical approach and has become widely used. In consequence, the microstrain fields rise and fall within the x-ray illuminated sample volume. This contrasts with so-called macrostrains which exceed the 1/5 scale and can cause a complete shift of a Bragg reflection from to a new lattice spacing do + ed. In this chapter only the reflection broadening due to microstrains is considered, whereas peak shifts due to macrostrains are postponed to Chapter 6.


line profile analysis (LPA) endeavors to derive microstructural features in the sample from the shape and broadening of Bragg reflections. Because broadening due to crystallite size and microstrain typically occur together, techniques were to develop that allow for the separation of both effects. These developments were mainly performed investigations of bulk material from metals or simple in organic compounds. LPA ideally requires diffraction patterns with a high signal-to noise (S/N) ratio and freestanding reflections with negligible overlap. In many cases the usage of Kal monochromatized radiation is recommended to obtain reliable results. It is evident from this listing that the applications of LPA to thin films may not be straightforward. Some ofthe following examples will therefore relate to powder samples, for which the techniques were originally developed. It has to be emphasized that the crystallite orientation distribution is assumed in many LPA approaches to be a random one. This presupposition is not generally fulfilled in polycrystalline thin films: rather, preferred orientation or texture is typically ob- served. This does not invalidate the application of LPA(lead glass window) techniques in principle, but it should carefully be checked as to how far the interpretation of the data would be affected texture effects.


This chapter follows the historical development of LPA in so far as size effects are presented first, while the analysis of concomitant size and strain broadening is outlined subsequently. It should be kept in mind, however, that thin-film samples typically exhibit both microstructural properties. Instrumental Box 4 is devoted to numerical methods and software techniques that are used in the analysis of x-ray scattering data. Nanocrystalline and nanocomposite materials are chosen as the material class for which the concepts of LPA are illustrated. In these materials new functionalities may be elicited, since the ratio of surface over bulk atoms may achieve unusually large values. Structure Box 4 covers crystalline lattice faults.

Line Profile Analysis

Soon after the invention of x-ray(x ray protection) diffraction it became dear that the method was not only suited to resolve crystalline structures, but could also reveal information on a sample's microstructure. In 1918 Scherrer devised a formula describing how the width of a Bragg reflection increases with decreasing crystallite size. The formula became very popular in the investigation of polycrystalline samples and made the crystallite size-peak width relation an ongoing issue in x-ray diffraction. It has to be emphasized, however, that the crystallite size derived from x-ray peak profiles accounts for domain sizes that scatter the incoming x-rays coherently. The size of coherently diffracting domains is generally smaller than the crystallite size as obtained by other techniques like transmission electron microscopy. It thus has to be carefully specified as to which experimental quantity is exactly meant whenever crystallite sizes are compared that have been obtained by different techniques.


The width of Bragg reflections was also realized to be affected by microstructural features other than size broadening, like the crystallite shape, the shape distribution and any distortion of the crystal structure like microstrain, dislocations,twin planes and stacking faults. The general question in the microstructural analysis of polycrystals relates to how the physical properties of the specimen are affected by its microstructure. It is evident that the microstructural richness of a polycrystalline thin film can become a hard task to be fully elucidated. The investigations are thus often restricted to certain aspects like the density of certain lattice faults.


Microstrain and dislocations play a prominent role in the various distortions of the crystal lattice. In the vicinity of dislocations the atoms reside on equilibrium po- sitions distinct from those in the unperturbed lattice and cause the surrounding bond lengths to contract and expand. The strain fields introduced by dislocations may extend over many hundreds of unit cells in the crystal. The interplanar spacing d as it appears in the Bragg equation is thus subjected to a variation and may not be accounted for by a fixed value do, but by a distribution of d values. The strain fields thus cause a smearing of scattered x-ray intensity around do and a broadening of reflections. These strain fields are denoted as microstrain, because they appear on a length scale that is small when compared with the inverse linear attenuation coefficient, 1/5, of the probing x ray beam. Although this definition is rather unsatisfactory, because a sample property is related to the technique by which it is probed, it is a practical approach and has become widely used. In consequence, the microstrain fields rise and fall within the x-ray illuminated sample volume. This contrasts with so-called macrostrains which exceed the 1/5 scale and can cause a complete shift of a Bragg reflection from to a new lattice spacing do + ed. In this chapter only the reflection broadening due to microstrains is considered, whereas peak shifts due to macrostrains are postponed to Chapter 6.


line profile analysis (LPA) endeavors to derive microstructural features in the sample from the shape and broadening of Bragg reflections. Because broadening due to crystallite size and microstrain typically occur together, techniques were to develop that allow for the separation of both effects. These developments were mainly performed investigations of bulk material from metals or simple in organic compounds. LPA ideally requires diffraction patterns with a high signal-to noise (S/N) ratio and freestanding reflections with negligible overlap. In many cases the usage of Kal monochromatized radiation is recommended to obtain reliable results. It is evident from this listing that the applications of LPA to thin films may not be straightforward. Some ofthe following examples will therefore relate to powder samples, for which the techniques were originally developed. It has to be emphasized that the crystallite orientation distribution is assumed in many LPA approaches to be a random one. This presupposition is not generally fulfilled in polycrystalline thin films: rather, preferred orientation or texture is typically ob- served. This does not invalidate the application of LPA(lead glass window) techniques in principle, but it should carefully be checked as to how far the interpretation of the data would be affected texture effects.


This chapter follows the historical development of LPA in so far as size effects are presented first, while the analysis of concomitant size and strain broadening is outlined subsequently. It should be kept in mind, however, that thin-film samples typically exhibit both microstructural properties. Instrumental Box 4 is devoted to numerical methods and software techniques that are used in the analysis of x-ray scattering data. Nanocrystalline and nanocomposite materials are chosen as the material class for which the concepts of LPA are illustrated. In these materials new functionalities may be elicited, since the ratio of surface over bulk atoms may achieve unusually large values. Structure Box 4 covers crystalline lattice faults.

Bruins' Gregory Campbell speaks for 1st time since breaking leg

Injured Bruins forward Gregory Campbell limped up to the podium, the very picture of Boston Strong.


Campbell has become part of hockey lore since breaking his leg blocking a shot while killing a penalty against the Pittsburgh Penguins in the Eastern final — and then finishing his shift. While Campbell downplays his heroics, coach Claude Julien says he epitomizes the blue-collar Bruins.


Campbell, who is on crutches(aluminum crutches price) after surgery June 10 to repair a broken right fibula, downplayed all of that when he met the media Tuesday at TD Garden. Asked about the legendary Bobby Baun, he said there was no comparison.


"I don't put myself in his category," Campbell said.


Baun scored the overtime winner for Toronto in Game 6 of the 1964 Stanley Cup final against Detroit despite breaking his foot midway through the third period after being hit by a Gordie Howe shot.


"I respect fully that feat of his," Campbell said. "And mine was nowhere near that. But it just goes to show you how tough you have to be to play in this league. There's 700, 800 players that are tough like that and play through things every day."


But Boston coach Claude Julien says Campbell epitomizes what the Bruins are all about: a blue-collar team that appreciates stars and role players alike.


'There's 18 other guys in that room that would do the same thing, and that's what makes us successful, and makes us a hard team to play against. I'd rather be known for my play other than getting hurt.'

— Injured Bruins forward Gregory Campbell

"That's how we've always been," he said.



With respect, Campbell refused to be singled out.


"Again, I'm not going to put myself in front of anybody else and say I'm the picture of the Bruins. This Original Six organization has gone back a long way," said the 29-year-old from London, Ont. "It kind of represents the city, a blue-collar hard-working city with honest people.


"So when I got traded to Boston, I thought it was tailor-made to my game the way this team exemplifies the heart and soul of what a hockey player should be made of. I was proud to come to this team and play hard for this team every night.


"There's 18 other guys in that room that would do the same thing, and that's what makes us successful, and makes us a hard team to play against. I'd rather be known for my play other than getting hurt."


Campbell, who centred the Bruins' fourth line between Daniel Paille and Shawn Thornton, said he knew something was up when he managed to get to his feet after blocking the shot.


"I don't have X-ray vision so I didn't know at the time that it was broken for sure," he said.


"It hurt a little bit. It was sore." he added. "But your adrenalin's going pretty good at that point. You're stuck on the ice with a couple of the best players in the world. You really don't have much time to think about anything else but trying to help out and kill the penalty."


Blue collar Bruins

The Bruins' work ethic is in high gear in the Stanley Cup final. They lead the Chicago Blackhawks two games to one going into Game 4 Wednesday night at TD Garden.


Like the city that is their home, the Bruins proudly show off their blue collar. And they have done so in the Stanley Cup final two our of the last three years.


The team rewards its player of the game after each win by having them wear an Army Ranger jacket that was given to defenceman Andrew Ference by a group of Rangers after the 2011 Cup win.


Boston's lunch-bucket attitude stood out in 2011 when they were matched against the aristocratic Canucks. This time, the stylish Blackhawks seems to have more speed and skill. But the Bruins are grinding them down.


"They have a little bit of everything," Chicago coach Joel Quenneville said admiringly of the Bruins. "You've got to commend them. They're a well-balanced team. They defend well. And they've got some offence as well."


The Bruins showed how close they are in the aftermath of Campbell's injury. The feisty forward said the entire team, as well as support staff, texted him every day.


Forward Brad Marchand said the team feels for Campbell and wants to win for him.


"We're all a family in here and we feel that pain that he's going through. It makes us want to dig down that much more for him."


That concern and affection hasn't stopped his teammates from giving him the gears, however. Campbell says his clothes often draw comment and Thornton was quick to pick on the pants he was wearing Tuesday.


"Thorty said the last time he saw a pair of white jeans was when he got in his last bar fight," said a laughing Campbell.


Responded Thornton: "You can't give him a break just because he's on crutches(pair of crutches). We're still boys here. You don't get a free pass."


Campbell, who made $1.4 million US this season, had four goals and nine assists in 48 games during the lockout-shortened season. He hopes to be healthy in time for training camp.

Bruins' Gregory Campbell speaks for 1st time since breaking leg

Injured Bruins forward Gregory Campbell limped up to the podium, the very picture of Boston Strong.


Campbell has become part of hockey lore since breaking his leg blocking a shot while killing a penalty against the Pittsburgh Penguins in the Eastern final — and then finishing his shift. While Campbell downplays his heroics, coach Claude Julien says he epitomizes the blue-collar Bruins.


Campbell, who is on crutches(aluminum crutches price) after surgery June 10 to repair a broken right fibula, downplayed all of that when he met the media Tuesday at TD Garden. Asked about the legendary Bobby Baun, he said there was no comparison.


"I don't put myself in his category," Campbell said.


Baun scored the overtime winner for Toronto in Game 6 of the 1964 Stanley Cup final against Detroit despite breaking his foot midway through the third period after being hit by a Gordie Howe shot.


"I respect fully that feat of his," Campbell said. "And mine was nowhere near that. But it just goes to show you how tough you have to be to play in this league. There's 700, 800 players that are tough like that and play through things every day."


But Boston coach Claude Julien says Campbell epitomizes what the Bruins are all about: a blue-collar team that appreciates stars and role players alike.


'There's 18 other guys in that room that would do the same thing, and that's what makes us successful, and makes us a hard team to play against. I'd rather be known for my play other than getting hurt.'

— Injured Bruins forward Gregory Campbell

"That's how we've always been," he said.



With respect, Campbell refused to be singled out.


"Again, I'm not going to put myself in front of anybody else and say I'm the picture of the Bruins. This Original Six organization has gone back a long way," said the 29-year-old from London, Ont. "It kind of represents the city, a blue-collar hard-working city with honest people.


"So when I got traded to Boston, I thought it was tailor-made to my game the way this team exemplifies the heart and soul of what a hockey player should be made of. I was proud to come to this team and play hard for this team every night.


"There's 18 other guys in that room that would do the same thing, and that's what makes us successful, and makes us a hard team to play against. I'd rather be known for my play other than getting hurt."


Campbell, who centred the Bruins' fourth line between Daniel Paille and Shawn Thornton, said he knew something was up when he managed to get to his feet after blocking the shot.


"I don't have X-ray vision so I didn't know at the time that it was broken for sure," he said.


"It hurt a little bit. It was sore." he added. "But your adrenalin's going pretty good at that point. You're stuck on the ice with a couple of the best players in the world. You really don't have much time to think about anything else but trying to help out and kill the penalty."


Blue collar Bruins

The Bruins' work ethic is in high gear in the Stanley Cup final. They lead the Chicago Blackhawks two games to one going into Game 4 Wednesday night at TD Garden.


Like the city that is their home, the Bruins proudly show off their blue collar. And they have done so in the Stanley Cup final two our of the last three years.


The team rewards its player of the game after each win by having them wear an Army Ranger jacket that was given to defenceman Andrew Ference by a group of Rangers after the 2011 Cup win.


Boston's lunch-bucket attitude stood out in 2011 when they were matched against the aristocratic Canucks. This time, the stylish Blackhawks seems to have more speed and skill. But the Bruins are grinding them down.


"They have a little bit of everything," Chicago coach Joel Quenneville said admiringly of the Bruins. "You've got to commend them. They're a well-balanced team. They defend well. And they've got some offence as well."


The Bruins showed how close they are in the aftermath of Campbell's injury. The feisty forward said the entire team, as well as support staff, texted him every day.


Forward Brad Marchand said the team feels for Campbell and wants to win for him.


"We're all a family in here and we feel that pain that he's going through. It makes us want to dig down that much more for him."


That concern and affection hasn't stopped his teammates from giving him the gears, however. Campbell says his clothes often draw comment and Thornton was quick to pick on the pants he was wearing Tuesday.


"Thorty said the last time he saw a pair of white jeans was when he got in his last bar fight," said a laughing Campbell.


Responded Thornton: "You can't give him a break just because he's on crutches(pair of crutches). We're still boys here. You don't get a free pass."


Campbell, who made $1.4 million US this season, had four goals and nine assists in 48 games during the lockout-shortened season. He hopes to be healthy in time for training camp.